Related papers: A Mathematical Picture Language Project
This poster summarizes our contributions to Wikimedia's processing pipeline for mathematical formulae. We describe how we have supported the transition from rendering formulae as course-grained PNG images in 2001 to providing modern…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
We present the approach underlying a course on "Domain-Specific Languages of Mathematics", currently being developed at Chalmers in response to difficulties faced by third-year students in learning and applying classical mathematics (mainly…
Predicting the future is of great interest across many aspects of human activity. Businesses are interested in future trends, traders are interested in future stock prices, and companies are highly interested in future technological…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the…
We present the training recipe and results of scaling up PaLI-X, a multilingual vision and language model, both in terms of size of the components and the breadth of its training task mixture. Our model achieves new levels of performance on…
Natural language provides a widely accessible and expressive interface for robotic agents. To understand language in complex environments, agents must reason about the full range of language inputs and their correspondence to the world.…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
Figures of speech help people express abstract concepts and evoke stronger emotions than literal expressions, thereby making texts more creative and engaging. Due to its pervasive and fundamental character, figurative language understanding…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
Computer simulation of languages is an old subject, but since the paper of Abrams and Strogatz (2003) several physics groups independently took up this field. We shortly review their work and bring more details on our own simulations.
This paper is devoted to present the Mathematics Grammar Library, a system for multilingual mathematical text processing. We explain the context in which it originated, its current design and functionality and the current development goals.…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
In natural language, words and phrases themselves imply the semantics. In contrast, the meaning of identifiers in mathematical formulae is undefined. Thus scientists must study the context to decode the meaning. The Mathematical Language…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…